78.8.31 problem 31

Internal problem ID [18229]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 31
Date solved : Tuesday, January 28, 2025 at 11:42:12 AM
CAS classification : [_separable]

\begin{align*} 3 x^{2} \ln \left (y\right )+\frac {x^{3} y^{\prime }}{y}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 11

dsolve(3*x^2*ln(y(x)) + x^3/y(x)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = {\mathrm e}^{-\frac {c_{1}}{x^{3}}} \]

✓ Solution by Mathematica

Time used: 0.168 (sec). Leaf size: 20

DSolve[3*x^2*Log[y[x]]+ x^3/y[x]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to e^{\frac {e^{c_1}}{x^3}} \\ y(x)\to 1 \\ \end{align*}